Nonlinear integrable systems constitute one of the most fascinating discoveries of applied mathematics and theoretical physics. The subject developed rapidly because of its wide applicabilty in a wide range of physical situations. It began with the study of shallow water waves in ﬂuid mechanics, and is now popular with both physicsts and mathematicians. Initial studies were conﬁned to the classical aspects of nonlinear partial diﬀerential equations, which were integrable. Later it was observed that their applicability could be extended to explain several phenomena in particle physics, condensed matter and even laser physics. Hence it was considered necessary to develop a quantum mechanical counterpart of the classical inverse scattering transform formalism.